Quark-hadron duality in lepton scattering off nucleons

Quark-hadron (QH) duality in lepton scattering off nucleons is studied with the resonance quark model. It is shown that in the case of neutrino scattering off an isoscalar target the duality is simultaneously observed for charged and neutral currents $xF_1^{\nu N}$, $F_2^{\nu N}$, and $xF_3^{\nu N}$ weak structure functions. We demonstrate that the QH duality can be useful property for modeling structure functions in the so-called resonance region. As an example it is shown that combining relativistic quark model predictions with duality arguments allows a construction of the inclusive resonance $F_2^{ep}$ structure function.Comment: 5 pages, 3 figures. Talk given at NuFact09, 11th International Workshop on Neutrino Factories, Superbeams and Beta Beams, July 20-25, 2009; IIT Chicago, US

Relevance of Two Boson Exchange Effect in Quasi-Elastic Charged Current Neutrino-Nucleon Interaction

Two boson exchange (TBE) correction to the cross section for the quasi-elastic charged current $\nu n$ and $\bar{\nu} p$ scattering is evaluated. The TBE is given by $W\gamma$ box diagrams. The calculations are performed for 1 GeV neutrinos. The averaged TBE correction is of the order of $2\div4$ (with respect to Born contribution) in the case of $\nu_e$ and $\bar{\nu}_e$ and $1\div2$ in the case of $\nu_\mu$ and $\bar{\nu}_\mu$. The impact of the TBE effect on the systematic discrepancy between the $\nu_e$ and $\nu_\mu$ cross sections is discussed.Comment: 6 pages, 7 figure

On the product formula on non-compact Grassmannians

We study the absolute continuity of the convolution $\delta_{e^X}^\natural \star \delta_{e^Y}^\natural$ of two orbital measures on the symmetric space SO_0(p,q)/SO(p)\timesSO(q), $q>p$. We prove sharp conditions on $X$, Y\in\a for the existence of the density of the convolution measure. This measure intervenes in the product formula for the spherical functions. We show that the sharp criterion developed for \SO_0(p,q)/\SO(p)\times\SO(q) will also serve for the spaces SU(p,q)/S(U(p)\timesU(q)) and Sp(p,q)/Sp(p)\timesSp(q), $q>p$. We also apply our results to the study of absolute continuity of convolution powers of an orbital measure $\delta_{e^X}^\natural$

On Wiener-Hopf factors for stable processes

We give a series representation of the logarithm of the bivariate Laplace exponent $\kappa$ of $\alpha$-stable processes for almost all $\alpha \in (0,2]$.Comment: 16 pages. to appear in Annales IHP, 201